Before starting school, many children reason logically about concepts that are basic to their later mathematical learning. We describe a measure of quantitative reasoning that was administered to children at school entry (mean age 5.8 years) and accounted for more variance in a mathematical attainment test than general cognitive ability 16 months…

Background: Several studies have examined young primary school children's use of strategies when solving simple addition and subtraction problems. Most of these studies have investigated students' strategy use as if they were isolated processes. To date, we have little knowledge about how math strategies in young students are related to other…

This study investigated "individual differences" in different aspects of early number concepts in preschoolers. Eighty 4-year-olds from Oxford nursery classes took part. They were tested on accuracy of counting sets of objects; the cardinal word principle; the order irrelevance principle; and predicting the results of repeated addition…

Two intervention studies are described. Both were designed to study the effects of teaching children about the inverse relation between addition and subtraction. The interventions were successful with 8-year-old children in Study 1 and to a limited extent with 5-year-old children in Study 2. In Study 1 teaching children about inversion increased…

In this article, the author describes a way of motivating learners to solve and reflect upon mathematical problems. The author wanted to find ways to help the Y6 class with their KS2 SATs, but more importantly she wanted to develop their interest and skills in solving mathematical challenges. She spent some time working on the idea of a "…

Investigates English students' strategies for addition and subtraction problems. Suggests some teaching methods for the results. (YP)

Reanalyzes data obtained in 1987 on mental calculation strategies used by 11-year-olds in England, Wales, and Northern Ireland. Classifies mental strategies developed in the past decade in international research. Compares frequency and effectiveness of the strategies used by pupils of different levels of attainment. Discusses basic arithmetic…

This paper considers whether or not curriculum initiatives within England are in fact leading to qualitatively improved levels of thinking among children identified as lower achievers in arithmetic. Revisiting data from two earlier studies and introducing current data, the paper draws comparisons in the strategies that 8-year-old children use to…

Interviewed 59 2nd- and 44 3rd-year elementary school students concerning their solutions to arithmetic problems commensurate with their age and ability. The results indicate that as children progress through school, they continue to use counting as an important part of their problem-solving repertoire, combining counting skills in idiosyncratic…